Let a be an n *1 matrix of real constants. How do you know `a^(')*a>=`0?

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Let A be an n x 1 matrix of real constants.

Let `A=[a_(i1)]_(nxx1), a_(i1)inRRAAi=1,2,..,n.`

`A'=[a_(1i)]_(1xxn)`

`Thus`

`A'.A=[b_(11)], where `

`b_(11)=a_(11).a_(11)+a_(21).a_(12)+....+a_(n1).a_(1n)`

`but a_(i1)=a_(1i),AAi=1,2,....,n.`

`b_(11)=(a_(11))^2+..........+(a_(1n))^2>=0`

`since`

`a_(i1)inRR,AA i=1,2,....n.`

`Thus`

`A'A=b11>=0.`

`=>A'A>=0`

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